1. Field of the Invention
The present invention relates generally to acoustic well logging. More particularly, the present invention relates to determining the velocity (slowness) of acoustic waves in an earth formation.
2. Description of the Related Art
In the art of acoustic logging, the formation properties of interest are one or more of the compressional wave velocity, the shear wave velocity and the Stonley wave velocity. These acoustic velocities are indicative of the formation's ability to hold and produce hydrocarbons. Operation of a typical acoustic formation tool may involve placing the tool in the well bore and firing one or more acoustic transmitters periodically, thus launching acoustic energy into the formation. The acoustic energy thus produced propagates along the formation wall in one or more propagation modes, e.g. compressional or shear wave modes. Receivers on the tool, spaced apart from the one or more transmitters, receive acoustic energy as the various waves move along the wall past the receivers. The amplitudes and arrival times of the various acoustic signals at the receivers are indicative of the velocity of the acoustic waves (or slowness, being the inverse of the velocity) within the formation.
Determining the acoustic velocity with early wireline acoustic logging tools involves an adaptation of data processing techniques used in seismic work. In particular, a method called semblance or coherence is used. U.S. Pat. No. 4,594,691 to Kimball et al. (hereinafter the '691 patent) is exemplary of related art wireline acoustic logging tools that use this semblance/coherence measure for determining acoustic velocities within the formation. As exemplified in the '691 patent, determining the acoustic velocity using a coherence calculation is just a determination of how much two or more received waveforms resemble one another. The semblance/coherence determination itself, however, is not at all concerned with actual formation properties; rather, the power of the semblance/coherence measure is running the calculation on portions of each received waveform that should correspond, given the slowness of the formation. Since the formation slowness is the parameter of interest, the semblance/coherence measure is run multiple times at multiple slowness values, and the slowness values where the waveforms show the best semblance/coherence are assumed to be the correct slowness values for the formation.
Although the semblance/coherence calculation method has been relatively successful, the oil and gas industry as a whole has been searching for different, better and more efficient ways to calculate acoustic velocity in earth formations. U.S. Pat. No. 5,541,890 to Tang (hereinafter the '890 patent) is exemplary of one such attempt. In particular, the '890 patent discloses that in the art of acoustic logging, any received signal may be synthesized by use of the other received signals. The '890 patent discloses synthesizing or estimating a received signal, and then comparing the synthesized signal to the actual received signal. For an array of possible slowness values, the '890 patent discloses creating an object function which is indicative of the difference between the synthesized received signal and the actual received signal. In the '890 patent, where that object function reaches a minimum (the difference between the synthesized signal and the actual signal are small), the values of the assumed slowness must match the actual formation slowness. Stated otherwise, the '890 patent records a series of waveforms at a plurality of receivers for each firing of the acoustic transmitter. The '890 patent then discloses synthesizing one received waveform from the remaining received waveforms, and comparing the synthesized received signal against the actual received signal.
A similar technique is disclosed in U.S. Pat. No. 5,081,611 to Hornby (hereinafter the '611 patent). The '611 patent discloses a method for determining slowness of an earth formation that involves calculating or estimating ray paths (ray tracing) and also estimating slowness values. The '611 patent discloses comparing the first arrivals (time of the first significant amplitude deflection in the received signal) predicted by the estimated ray path and slowness values to the actual first arrivals in each received signal. The patent discloses “back projecting” the error between the actual and calculated first arrivals (here again in the received signals) and running the process of estimating ray paths and slowness values again until the error is small, thus revealing the actual ray paths and formation slowness. Much like the '890 patent described above, the '611 patent is effectively estimating received signals, and comparing those estimated received signals to the actual received signals as part of determining slowness.
While semblance/coherence may create visually pleasing results, determining slowness in this matter is not suitable for error estimation. Techniques described in the '611 patent and the '890 patent disclosures may suffer from the same shortcomings. Consequently, an improved method to determine the velocity or slowness of the various propagation modes in an earth formation is desired.